Some properties of the solution of a filtration problem in partially saturated porous media

A filtration problem with second initial-boundary value in partially saturated porous media is considered, In addition to discussion of the existence and uniqueness of weak solution of the problem, it is demonstrated that the interface between the saturated and unsaturated regions exists and continues under certain conditions and the solution possesses some properties, e.g., the balance of water content, the time-limit existence of weak solution ect. which differ from those of the solutions of the first initial-boundary value problem.